Recently, certain poly (N-acylethyleneimine) grafted polysiloxanes have been watched with great interest as one of the most prominent surfactants, lubricants and resin compatibility modifiers. This is because they each have a specific molecular structure wherein a hydrophilic portion of poly N-acylethyleneimine and a hydrophobic portion of polysiloxane are maldistributed in the same molecule. Such polysiloxanes of the formula ##STR1## were first reported by Mr. Takeo Saegusa, at the meeting of Japan Chemical Society, Spring Session 54, (abstract of said lecture was published 1987). According to the synthetic method proposed by Mr. Saegusa, a vinyl group-containing tosyl ester is reacted with oxazoline to give a vinyl group-containing poly N-acylethyleneimine compound, and the latter is then reacted with polysiloxane in the presence of platinic acid catalyst, thereby effecting addition reaction of the SiH portion of said polysiloxane and said vinyl group to give the desired grafted polysiloxane. However, in that method, there are many problems still awaiting solutions. That is, (1) since an allyl tosylate is thermally and chemically unstable, there often occurs under oxazoline's ring-opening polymerization conditions, such side-reaction as polymerization of the double bond, (2) since the involved reaction is the reaction between polymer and polymer (i.e. poly N-acylethyleneimine compound and polysiloxane), determination of appropriate solvent and other reaction conditions are considerably difficult to do, (3) since the poly N-acylethyleneimine compound carries hydroxyl groups, the addition reaction with silane compound in the presence of platinic acid catalyst is hindered by said hydroxyl groups, and (4) since poly N-acylethyleneimine is prepared by the reaction of tosyl ester and oxazoline, it must be separated from the reaction mixture and purified before using it in the subsequent addition reaction, or otherwise the remaining tosyl groups will hinder said addition reaction. Furthermore, the poly (N-acylethyleneimine) grafted polysiloxanes disclosed in the abovementioned report do not have any functional groups other than N-acylethyleneimine. Therefore, even if a novel class of polysiloxane derivatives is desired for additional objects as, for example, solubility regulation activity, reactivity or the like, it is essential to introduce the desired functional groups into the polysiloxane molecule by adopting a series of complicated reaction means. It is, therefore, an object of the invention to provide a novel process for the preparation of poly (N-acylethyleneimine) grafted polysiloxanes, which is free from the abovementioned problems and easily applicable to an industrial scale of production of said grafted polysiloxanes. A further object of the invention is to provide a novel class of poly (N-acylethyleneimine) grafted polysiloxanes having additional functional groups other than N-acylethyleneimine.